9,666 research outputs found
Can one determine cosmological parameters from multi-plane strong lens systems?
Strong gravitational lensing of sources with different redshifts has been
used to determine cosmological distance ratios, which in turn depend on the
expansion history. Hence, such systems are viewed as potential tools for
constraining cosmological parameters. Here we show that in lens systems with
two distinct source redshifts, of which the nearest one contributes to the
light deflection towards the more distant one, there exists an invariance
transformation which leaves all strong lensing observables unchanged (except
the product of time delay and Hubble constant), generalizing the well-known
mass-sheet transformation in single plane lens systems. The transformation
preserves the relative distribution of mass and light, so that a
`mass-follows-light' assumption does not fix the MST. All time delays (from
sources on both planes) scale with the same factor -- time-delay ratios are
therefore invariant under the MST. Changing cosmological parameters, and thus
distance ratios, is essentially equivalent to such a mass-sheet transformation.
As an example, we discuss the double source plane system SDSSJ0946+1006, which
has been recently studied by Collett and Auger, and show that variations of
cosmological parameters within reasonable ranges lead to only a small
mass-sheet transformation in both lens planes. Hence, the ability to extract
cosmological information from such systems depends heavily on the ability to
break the mass-sheet degeneracy.Comment: 5 pages, matches the printed versio
The cosmological lens equation and the equivalent single-plane gravitational lens
The gravitational lens equation resulting from a single (non-linear) mass
concentration (the main lens) plus inhomogeneities of the large-scale structure
is shown to be strictly equivalent to the single-plane gravitational lens
equation without the cosmological perturbations. The deflection potential (and,
by applying the Poisson equation, also the mass distribution) of the equivalent
single-plane lens is derived. If the main lens is described by elliptical
isopotential curves plus a shear term, the equivalent single-plane lens will be
of the same form. Due to the equivalence shown, the determination of the Hubble
constant from time delay measurements is affected by the same mass-sheet
invariance transformation as for the single-plane lens. If the lens strength is
fixed (e.g., by measuring the velocity dispersion of stars in the main lens),
the determination of is affected by inhomogeneous matter between us and
the lens. The orientation of the mass distribution relative to the image
positions is the same for the cosmological lens situation and the single-plane
case. In particular this implies that cosmic shear cannot account for a
misalignment of the observed galaxy orientation relative to the best-fitting
lens model.Comment: TeX, 11 pages, submitted to MNRA
Mass-sheet degeneracy, power-law models and external convergence: Impact on the determination of the Hubble constant from gravitational lensing
The light travel time differences in strong gravitational lensing systems
allows an independent determination of the Hubble constant. This method has
been successfully applied to several lens systems. The formally most precise
measurements are, however, in tension with the recent determination of
from the Planck satellite for a spatially flat six-parameters
cosmology. We reconsider the uncertainties of the method, concerning the mass
profile of the lens galaxies, and show that the formal precision relies on the
assumption that the mass profile is a perfect power law. Simple analytical
arguments and numerical experiments reveal that mass-sheet like transformations
yield significant freedom in choosing the mass profile, even when exquisite
Einstein rings are observed. Furthermore, the characterization of the
environment of the lens does not break that degeneracy which is not physically
linked to extrinsic convergence. We present an illustrative example where the
multiple imaging properties of a composite (baryons + dark matter) lens can be
extremely well reproduced by a power-law model having the same velocity
dispersion, but with predictions for the Hubble constant that deviate by . Hence we conclude that the impact of degeneracies between parametrized
models have been underestimated in current measurements from lensing, and
need to be carefully reconsidered.Comment: Accepted for publication in Astronomy and Astrophysics. Discussion
expanded (MSD and velocity dispersion, MSD and free form lens models, MSD and
multiple source redshifts
U(g)-finite locally analytic representations
In this paper we continue the study of locally analytic representations of a
-adic Lie group in vector spaces over a spherically complete
non-archimedean field , building on the algebraic approach to such
representations introduced in our paper "Locally analytic distributions and
p-adic representation theory, with applications to GL_2." In that paper we
associated to a representation a module over the ring of
locally analytic distributions on and described an admissibility condition
on in terms of algebraic properties of .
In this paper we determine the relationship between our admissibility
condition on locally analytic modules and the traditional admissibility of
Langlands theory. We then analyze the class of locally analytic representations
with the property that their associated modules are annihilated by an ideal of
finite codimension in the universal enveloping algebra of G, showing under some
hypotheses on G that they are sums of representations of the form ,
with X finite dimensional and Y smooth. The irreducible representations of this
type are obtained when X and Y are irreducible.
We conclude by analyzing the reducible members of the locally analytic
principal series of SL_2(\Qp)
The lightcurve reconstruction method for measuring the time delay of gravitational lens systems
We propose a new technique to measure the time delay of radio-loud
gravitational lens systems, which does not rely on the excessive use of
interferometric observations. Instead, the method is based on single-dish flux
density monitoring of the (unresolved) lens system's total lightcurve, combined
with additional interferometric measurements of the flux density ratio at a few
epochs during that monitoring period. The basic idea of the method is to
reconstruct the individual image lightcurves from the observed total lightcurve
by assuming a range of potential values for the time delay and the
magnification ratio of the images. It is then possible to single out the
correct reconstruction, and therefore determine the time delay, by checking the
consistency of the reconstructed individual lightcurves with the additional
interferometric observations. We performed extensive numerical simulations of
synthetic lightcurves to investigate the dependence of the performance of this
method on various parameters which are involved in the problem. Probably the
most promising candidates for applying the method (and also for determining the
Hubble constant) are lens systems consisting of multiply imaged compact sources
and an Einstein ring, such as B0218+357 from which some of the parameters used
for our simulations were adopted.Comment: 26 pages, LaTex, including 23 figures; submitted to Monthly Notices
of the Royal Astronomical Society; a version with a higher quality for some
of the figures is available at
http://www.mpa-garching.mpg.de/Lenses/Preprints/LightCrv.ps.g
Aperture Multipole Moments from Weak Gravitational Lensing
The projected mass of a gravitational lens inside (circular) apertures can be
derived from the measured shear inside an annulus which is caused by the tidal
field of the deflecting mass distribution. Here we show that also the
multipoles of the two-dimensional mass distribution can be derived from the
shear in annuli. We derive several expressions for these mass multipole moments
in terms of the shear, which allow large flexibility in the choice of a radial
weight function. In contrast to determining multipole moments from weak-lensing
mass reconstructions, this approach allows to quantify the signal-to-noise
ratio of the multipole moments directly from the observed galaxy ellipticities,
and thus to estimate the significance of the multipole detection. Radial weight
functions can therefore be chosen such as to optimize the significance of the
detection given an assumed radial mass profile. Application of our formulae to
numerically simulated clusters demonstrates that the quadrupole moment of
realistic cluster models can be detected with high signal-to-noise ratio S/N;
in about 85 per cent of the simulated cluster fields S/N >~ 3. We also show
that the shear inside a circular annulus determines multipole moments inside
and outside the annulus. This is relevant for clusters whose central region is
too bright to allow the observation of the shear of background galaxies, or
which extend beyond the CCD. We also generalize the aperture mass equation to
the case of `radial' weight functions which are constant on arbitrarily-shaped
curves which are not necessarily self-similar.Comment: 14 pages including 3 figures; submitted to MNRAS; replaced to improve
printing on non-A4 pape
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